On Cygwin using non-managed mounts (and presumably other operating systems when using a case-insensitive file system), it's not possible to use Coreutils mv to change the case of a filename; mv reports that they are the same file.

The underlying Cygwin rename() function does support this functionality.

$ touch foo
$ mv foo Foo
mv: `foo' and `Foo' are the same file
$ mv --version
mv (GNU coreutils) 6.9
Copyright (C) 2007 Free Software Foundation, Inc.
This is free software. You may redistribute copies of it under the terms of
the GNU General Public License <http://www.gnu.org/licenses/gpl.html>.
There is NO WARRANTY, to the extent permitted by law.